# "So we have the action defined in (I), and an (alternative)" ## "definition of normalizer in (II). Additionally, we have the" ## "stabilizer of a subset" \ A sube S, "which is the set of elements of" \ \ G, "that leave" \ A \ \ "fixed under the action" \ \ \alpha:" #

# "From the beginning, keep in mind that, in the stabilizer," ## "what is being stabilized (left fixed) is the subset" \ A sube S. #

# "Also, in the language I think you used, you interpreted the" ## "stabilizer as:" \qquad "the set of elements of" \ \ G,"where" \ A \ \ "acts" ## "like an identity on" \ \ G. \ \ "This is not to criticize -- this is a" ## "good way of being able to think of things. From this point of" ## "view, the interpretation would be:" \qquad "the stabilizer is the set of" ## "elements of" \ \ G,"that act like an identity on" \ A. #

# "2) Unless basic hygiene is applied, notation for actions can" ## "quickly result in confusion, or obfuscation of what's happening." ## "For example, in the unfortunate standard action notation, the" ## "action of the element" \ g \in G, "on the subset" \ \ A sube S, "is [crazy]" ## "denoted:" \ \ gA. \ \ "It looks to all the world like group" ## "multiplication, but is not meant to be. For example, with this" ## "notation, the particular action we have been using here would" ## "be written:" #